```Haskell import System.Random

– Exercício 1

inits :: [a] -> [[a]] inits [] = [[]] inits l = inits (init l) ++ [l]

isPrefixOf :: Eq a => [a] -> [a] -> Bool isPrefixOf [] _ = True isPrefixOf _ [] = False isPrefixOf (h:t) (h’:t’) = h == h’ && isPrefixOf t t’

– Exercício 2

data BTree a = Empty

Node a (BTree a) (BTree a) deriving Show

tree :: BTree Int tree = Node 5 (Node 2 (Node 1 Empty Empty) (Node 3 Empty Empty)) (Node 8 (Node 7 (Node 6 Empty Empty) Empty) (Node 9 Empty Empty))

{- 5 / \
/
2 8 / \ /
1 3 7 9 / 6 -}

folhas :: BTree a -> Int folhas Empty = 0 folhas (Node _ Empty Empty) = 1 folhas (Node _ l r) = folhas l + folhas r

path :: [Bool] -> BTree a -> [a] path _ Empty = [] path [] (Node a _ _) = [a] path (h:t) (Node a l r) = a:path t (if h then r else l)

– Exercício 3

type Polinomio = [Coeficiente] type Coeficiente = Float

pol :: Polinomio pol = [0,0,0,-5,0,2]

valor :: Polinomio -> Float -> Float valor p x = foldr (\e -> (+) $ snd e * x ^ fst e) 0 (zip [0..] p)

valor’ :: Polinomio -> Float -> Float valor’ p x = sum (zipWith (\a b -> b * x ^ a) [0..] p)

deriv :: Polinomio -> Polinomio deriv = tail . zipWith (*) [0..]

soma :: Polinomio -> Polinomio -> Polinomio soma = zipWith (+)

– Exercício 4

type Mat a = [[a]]

ex = [[1,4,3,2,5],[6,7,8,9,0],[3,5,4,9,1]]

quebraLinha :: [Int] -> [a] -> [[a]] quebraLinha [] _ = [] quebraLinha (h:t) l = take h l : quebraLinha t (drop h l)

quebraLinhas :: [Int] -> Mat a -> [Mat a] quebraLinhas [] _ = [] quebraLinhas (h:t) m = map (take h) m : quebraLinhas t (map (drop h) m)

fragmenta :: [Int] -> [Int] -> Mat a -> [Mat a] fragmenta [] _ _ = [] fragmenta (h:t) pc m = quebraLinhas pc (take h m) ++ fragmenta t pc (drop h m)

geraLinha :: Int -> (Int, Int) -> IO [Int] geraLinha 0 _ = return [] geraLinha x r = fmap (flip (:)) (geraLinha (x-1) r) <*> randomRIO r {- geraLinha x r = do t <- geraLinha (x-1) r randomRIO r »= (return . flip (:) t) -}

{- geraLinha x r = do t <- geraLinha (x-1) r n <- randomRIO r return $ n : t -}

geraMat :: (Int, Int) -> (Int, Int) -> IO (Mat Int) geraMat (0,_) _ = return [] geraMat (x,y) r = fmap (flip (:)) (geraMat (x-1,y) r) <*> geraLinha y r

{- geraMat (x,y) r = do m <- geraMat (x-1,y) r l <- geraLinha y r return $ l : m -}